Identifying Integers and Their Opposites. ESSENTIAL QUESTION How do you identify an integer and its opposite? Positive integers
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1 LESSON 1.1 Identifying Integers and Their Opposites Number and operations Identify a number, its opposite, and its absolute value.? ESSENTIL QUESTION How do you identify an integer and its opposite? EXPLORE CTIVITY 1 Positive and Negative Numbers Positive numbers are numbers greater than 0. Positive numbers can be written with or without a plus sign; for example, 3 is the same as +3. Negative numbers are numbers less than 0. Negative numbers must always be written with a negative sign. The number 0 is neither positive nor negative Image Credits: Corbis Negative integers Positive integers The elevation of a location describes its height above or below sea level, which has elevation 0. Elevations below sea level are represented by negative numbers, and elevations above sea level are represented by positive numbers. C D The table shows the elevations of several locations in a state park. Graph the locations on the number line according to their elevations. Location Little utte Cradle Creek Dinosaur Valley C Mesa Ridge D Juniper Trail E Elevation (ft) What point on the number line represents sea level? Which location is closest to sea level? How do you know? Which two locations are the same distance from sea level? re these locations above or below sea level? E Which location has the least elevation? How do you know? Lesson 1.1 7
2 EXPLORE CTIVITY 1 (cont d) Reflect 1. nalyze Relationships Morning Glory Stream is 7 feet below sea level. What number represents the elevation of Morning Glory Stream? 2. Multiple Representations Explain how to graph the elevation of Morning Glory Stream on a number line. EXPLORE CTIVITY 2 Opposites Two numbers are opposites if, on a number line, they are the same distance from 0 but on different sides of 0. For example, 5 and -5 are opposites. 0 is its own opposite. Integers are the set of all whole numbers and their opposites. On graph paper, use a ruler or straightedge to draw a number line. Label the number line with each integer from -10 to 10. Fold your number line in half so that the crease goes through 0. Numbers that line up after folding the number line are opposites Remember, the set of whole numbers is 0, 1, 2, 3, 4, 5, 6,... Use your number line to find the opposites of 7, -6, 1, and 9. How does your number line show that 0 is its own opposite? C What is the opposite of the opposite of 3? Reflect 3. Justify Reasoning Explain how your number line shows that 8 and -8 are opposites. 4. Multiple Representations Explain how to use your number line to find the opposite of the opposite of Unit 1
3 Integers and Opposites on a Number Line Positive and negative numbers can be used to represent real-world quantities. For example, 3 can represent a temperature that is 3 F above can represent a temperature that is 3 F below 0. oth 3 and -3 are 3 units from 0. Math On the Spot my.hrw.com EXMPLE 1 Sandy kept track of the weekly low temperature in her town for several weeks. The table shows the low temperature in F for each week. Week Week 1 Week 2 Week 3 Week 4 Temperature ( F) My Notes Use this space to take notes as you listen in class. Graph the temperature from Week 3 and its opposite on a number line. What do the numbers represent? STEP 1 STEP 2 Graph the value from Week 3 on the number line. The value from Week 3 is -4. Graph a point 4 units below 0. Graph the opposite of -4. Graph a point 4 units above 0. The opposite of -4 is represents a temperature that is 4 F below 0 and 4 represents a temperature that is 4 F above 0. The value for Week 5 is the opposite of the opposite of the value from Week 1. What was the low temperature in Week 5? STEP 1 STEP 2 STEP 3 Graph the value from Week 1 on the number line. The value from Week 1 is -1. Graph the opposite of -1. The opposite of -1 is 1. Graph the opposite of 1. The opposite of 1 is The opposite of the opposite of -1 is -1. The low temperature in Week 5 was -1 F. Reflect 5. nalyze Relationships Explain how you can find the opposite of the opposite of any number without using a number line. Lesson 1.1 9
4 YOUR TURN Personal Math Trainer Online ssessment and Intervention my.hrw.com Graph the opposite of the number shown on each number line Math Talk Mathematical Processes Explain how you could use a number line to find the opposite of 8. Guided Practice Write the opposite of each number What is the opposite of the opposite of 6? 1. Graph and label the following points on the number line. (Explore ctivity 1) a. -2 b. 9 c. -8 d. -9 e. 5 f Graph the opposite of the number shown on each number line. (Explore ctivity 2 and Example 1) Write the opposite of each number. (Explore ctivity 2 and Example 1)? ESSENTIL QUESTION CHECK-IN 11. Given an integer, how do you find its opposite? 10 Unit 1
5 Name Class Date 1.1 Independent Practice my.hrw.com Personal Math Trainer Online ssessment and Intervention 12. Chemistry toms normally have an electric charge of 0. Certain conditions, such as static, can cause atoms to have a positive or a negative charge. toms with a positive or negative charge are called ions. Ion C D E Charge a. Which ions have a negative charge? b. Which ions have charges that are opposites? c. Which ion s charge is not the opposite of another ion s charge? Name the integer that meets the given description. 13. the opposite of units left of the opposite of the opposite of units right of units right of the opposite of nalyze Relationships Several wrestlers are trying to lose weight for a competition. Their change in weight since last week is shown in the chart. Wrestler Tino Victor Ramsey axter Luis Weight Change (in pounds) a. Did Victor lose or gain weight since last week? b. Which wrestler s weight change is the opposite of Ramsey s? c. Which wrestlers have lost weight since last week? d. Frankie s weight change since last week was the opposite of Victor s. What was Frankie s weight change? e. Frankie s goal last week was to gain weight. Did he meet his goal? Explain. Lesson
6 Find the distance between the given number and its opposite on a number line What If? Three contestants are competing on a trivia game show. The table shows their scores before the final question. a. How many points must Shawna earn for her score to be the opposite of Timothy s score before the final question? b. Which person s score is closest to 0? c. Who do you think is winning the game before the final question? Explain. Contestant Score efore Final Question Timothy -25 Shawna 18 Kaylynn -14 FOCUS ON HIGHER ORDER THINKING Work rea 25. Communicate Mathematical Ideas Which number is farther from 0 on a number line: -9 or 6? Explain your reasoning. 26. nalyze Relationships number is k units to the left of 0 on the number line. Describe the location of its opposite. 27. Critique Reasoning Roberto says that the opposite of a certain integer is -5. Cindy concludes that the opposite of an integer is always negative. Explain Cindy s error. 28. Multiple Representations Explain how to use a number line to find the opposites of the integers 3 units away from Unit 1
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